Question: Simplify to lowest terms. $\dfrac{48}{42}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 48 and 42? $48 = 2\cdot2\cdot2\cdot2\cdot3$ $42 = 2\cdot3\cdot7$ $\mbox{GCD}(48, 42) = 2\cdot3 = 6$ $\dfrac{48}{42} = \dfrac{8 \cdot 6}{ 7\cdot 6}$ $\hphantom{\dfrac{48}{42}} = \dfrac{8}{7} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{48}{42}} = \dfrac{8}{7} \cdot 1$ $\hphantom{\dfrac{48}{42}} = \dfrac{8}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{48}{42}= \dfrac{2\cdot24}{2\cdot21}= \dfrac{2\cdot 3\cdot8}{2\cdot 3\cdot7}= \dfrac{8}{7}$